Questions tagged [mathematical-economics]

The application of mathematical methods to represent theories and analyze problems in economics.

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1answer
53 views

What does it mean when we say an iso curve has no interior?

From the paper: "Standard Auctions with Financially Constrained Bidders" - by Che and Gale. The authors describe an isobid curve as the curve that represents payments of the same value in a 2-...
3
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1answer
588 views

Solow growth model - analytic proof that Inada conditions imply steady state capital is increasing in the savings rate

Let's take the example of a generic Harrod-neutral (labor-augmenting) production function $f(k)$; all letters denote the growth rates they usually would. In the regular Solow growth model with the ...
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2answers
170 views

Is economics Turing Complete?

I am interested in economics from the perspective of mathematical physics and complexity theory. An important set of systems in complex systems are systems that are Turing Complete and are cases of ...
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0answers
124 views

Does a determinant ever have its own interpretation in economics?

I know there are applications of determinants in economics to compute equilibrium, aide in identifying profit maximisation/cost minimisation and in calculating elasticity of substitution. However, is ...
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1answer
215 views

Properties of preference relation

Let $\succeq$ be a preference relation on $X$. Is it true that $x \succeq y$ if and only if $\lnot (y \succ x)$? I think it is true and my proof is as follows. To prove $\implies$ direction, we have ...
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0answers
352 views

What does Sims' critique of economics models actually say?

I've been searching for answer, but I can't find a clear cut one. From what I understand it says that, in the realistic model there are no exogenous variables? Or does it say that there can be no ...
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1answer
468 views

What determines if a variable is exogenous or endogenous in a model? [duplicate]

Question above, I have a very rudimentary understanding of econometrics.
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1answer
2k views

What is Saddle Point Stability?

What is saddle point stability and what sorts of functions or systems of equations give rise to such a thing? For example, would we say that a two systems of stochastic difference equations that are ...
7
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1answer
198 views

Optimization: Dynamic Programming vs Kuhn-Tucker

Considering the standard utility maximization of representative household which lives forever, one may use dynamic programming and Kuhn-Tucker in case of discrete time. For instance, one would like to ...
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0answers
80 views

Visualising eigenvectors/values

This might seem like an odd question but seeing as I haven't had any formal education in solving ratex models yet, it is something I have been thinking about a lot recently. Consider the following ...
5
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2answers
83 views

Multidimensional screening and convexity of the surplus/rent function

I'm starting to read the literature of multidimensional screening models for monopolists selling $n$ goods to a continuum of buyers with $m=n$ dimensional types, and Rochet (1987) proves that a ...
3
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2answers
121 views

Budget hyperplane in n dimensions

Take the set of all vectors $x = (x_1, \cdots, x_n)$ that are solutions to $p_1x_1 + \cdots + p_nx_n = I > 0$. Show that this set has $n-1$ dimensions. I have somehow managed to get myself ...
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2answers
329 views

Quantitative Marxian/Marxist micro and macro economic models?

Are there quantitative Marxian/Marxist/neo-Marxist economic models like Dynamic Stochastic General Equilibrium models or Euro Area Wide (micro-founded) models - that can be used by central banks and ...
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1answer
45 views

Simplifying a monoplist's objective function under incomplete information

I am working through Rochet and Stohle (2003) chapter on multi-dimensional screening, and I am struggling filling in the blanks between equation (2.1) p. 154, and its simplified form on page 155. In ...
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0answers
47 views

Common knowledge in model formulation and solution

Economics models usually assume that the structure of the economy is common knowledge among agents. Mathematically, an event is common knowledge if it lies in the meet of all agents' information ...
5
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1answer
145 views

Interpretation of utility function

I am reading Lucas (1980) and I am a bit confused about the way he formulates the utility function. So there is one non-storable good that comes in $n$ colours and one unit of labor produces $y$ ...
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1answer
188 views

Auction and best response

Consider an auction in which $k$ identical objects are sold to $ n>k $ bidders. Each bidder $i$ needs only one object and has a valuation $v_{i}$ for the object. In the auction, simultaneously, ...
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3answers
6k views

Mathematical derivation of the Production Possibility Frontier

What are the mathematical basics of production possibility frontier? How can I derivate it? Can I have an example for it?
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0answers
39 views

Question on a sufficient condition of contractiveness of best reply functions in Vives (1999)

I have trouble in understanding why a sufficient condition that a best reply function is a contraction. The following is a screenshot of Xavier Vives's Oligopoly Pricing: Old Ideas and New Tools from ...
5
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1answer
99 views

Higher order beliefs and coherency in game theory

I am reading about the higher order beliefs. Before getting into the formal definitions, I will define some common terminology which I will need for the formal definitions. If $X$ and $Y$ are two ...
6
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1answer
207 views

Where do the rich and poor live in a city? (Calculus)

I am reading 'Cities, Agglomeration and Spatial Equilibrium' by Ed Glaeser. People live in a monocentric city, where consumers of heterogeneous income $y$ work at the centre of the city. They buy $H(...
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1answer
191 views

How to make a timeline in given problem?

How much money should be deposited each year for 12 years if you wish to withdraw $309 each year for five years, beginning at the end of the 14th year? Let i = 8% per year. In the problem what ...
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1answer
2k views

How can I show that the following function is homothetic? [duplicate]

$y= (x_1x_2)^2-x_1x_2$ Let $x_1x_2=z$ then $y=z^2-z$ and $y'=2z-1$ If I can prove that y' is monotonically increasing, does that prove y is a homothetic function? if so then how can I prove that y' ...
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0answers
197 views

Bayes Nash Equilibrium in a game with continuous actions

I am attempting to think through a particular type of game with continuous strategies, with Bayes Nash equilibrium as the solution concept. I first describe the game below, followed by questions. ...
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1answer
30 views

Where can I find historical (very old) USD printing data?

Where can I find historical/very old USD printing data? Charts can be useful, but I want numbers. It is for a project.
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0answers
94 views

Elasticities and exponents

Given the following 3 equations: $$ Y^*_t=100+3t \\ Y_t = Y_t^* (1+(0.2 (\sin t)) \\ B_t=B_t^* (1+(0.4 (\sin t)) \\ $$ And take B* to be the following, but is unknown: $$ B_t^*= \alpha Y_t^* \\ $$ I'...
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1answer
128 views

Can Ramanujan Sum : 1+2+3+4+5+… = -1/12 be used to explain some results in macro-economics? [closed]

In this youtube video the speakers present a line of reasoning as to why $$ \sum_{n=1}^\infty n = -\frac{1}{12} $$ in other words $$1+2+3+\cdots=-\frac{1}{12}$$ and my brain still hurts. It ...
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2answers
325 views

Prove that variance of a portfolio cannot exceed variance of individual assets

When reading on Markowitz's portfolio theory, I stumbled across the fact that in a market with two risky assets, if no short selling is not allowed, the variance of a portfolio consisting of the two ...
2
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1answer
135 views

What does non degeneracy mean for a preference?

I saw a non-degeneracy assumption in Gilboa and Schmeidler's paper (maxmin expected utility with non-unique prior). The statement is "Not for all $f$ and $g$ in $L$, $f \geq g$". So can you explain ...
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1answer
797 views

Game Theory Question

| | |Adv| ---------|N\A| Adv| 300,300 | 900,0 | N\A| 0,900 | 700,700 | Player 1= Pepsi Player 2= Coke A) Solve for the pure strategy Nash equilibrium B) Is this ...
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1answer
485 views

What are the fundamental economic proofs

We had a question on this site for Fundamental equations in economics. What I'd like to know is what are the most important proofs needed in economics?
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1answer
543 views

Applications to Green's Theorem in Economics?

I was wondering about possible of application of integration to economics (other than welfare), more specifically, how might Green's theorem be useful for an economist? Let C be a positively oriented,...
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2answers
488 views

Preference for consumption smoothing and actual smoothing

The typical dynamic consumption-saving under certainty model can be written as: $$ \max V(c)=\sum_{t=1}^{T} \beta^{t-1}\; u(c_t) $$ Subject to the intertemporal budget constraint $$ \sum_{t=1}^{T}\...
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475 views

Calculus and Indifference Curves in an Urban Economics Example

I am reading the paper 'The Structure of Urban Equilibria' by Jan Brueckner. It uses a monocentric city model, where all consumers earn income $y$ at the centre of the city. They buy $q$ housing for ...
3
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1answer
2k views

Positive Monotonic Transformations and Nested Functions

Suppose there is an economic agent with the utility function $u(x,y)$. A second agent has the utility function $h(g(f(u(x,y))))$. Am I correct in thinking that if $f'(x)>0$, $g'(x)>0$, and $h'(...
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0answers
256 views

How accurate is duality?

In economic theory we know that with the use of some calculus, Hotellings Lemma and Sheppards lemma we can derive a given firms supply function and in term its Profit function. With data of a given ...
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1answer
264 views

Wooldridge's Microeconomics book vs Cameron and Trivedi's textbook

I'm debating between 2 Microeconometric classes at my college, (I realize I'm fortunate to have a choice). One class uses Wooldridge's "Econometric Analysis of Cross Section and Panel Data" the other ...
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0answers
62 views

Rent gradient in Alonso-Muth-Mills monocentric city with two transport technologies

Consider a mono-centric city, where all workers earn a wage $W$ in the centre of the circular city and rent out land $L$. Rent $r(d)$ and transport costs $t(d)$ vary with distance from the centre, $d$...
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1answer
491 views

Derivation long run cost function of three inputs with Leontief-like characteristics

Suppose that a firm produces a good using capital, skilled labor, and unskilled labor. Let $K$ denote the amount of capital,$L_1$ unskilled labor, $L_2$ skilled labor. The production function is $f(...
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1answer
1k views

Total Differential of a Utility Function Subject to a Budget Constraint

I am trying to fully understand the process of maximizing a utility function subject to a budget constraint while utilizing the Substitution Method (as opposed to the Lagrangian Method). I am ...
3
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1answer
171 views

Arrow-Debreu Pricing, Planner's Problem

Consider a two period, single good, $2$ agent model. Time beings in perios $0$ in a known state (state $0$) but in period $1$ the world may find itself in any one of two states $s = 1,2$ with ...
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0answers
48 views

What model did the MONIAC use?

Phillips designed a hydraulic computer to model the UK economy in 1949; 12-14 copies were built. What model did it compute with? How have modern models of the UK built on that work?
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0answers
28 views

How do We Determine the Start or End of Investment Phase for the Oil Industry

I am trying to do an analysis of the oil industry, and while doing research I came across the following chart that has one of the factors I want to include: Investment Phase vs Exploitation Phase The ...
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0answers
581 views

Euler's Homogenous Function Theorem with elasticity

I'm currently reviewing my prof's slides in preparation for an exam. In one of them, he talks about Euler's Homogenous Function Theorem: Let $f(x_1, x_2, ..., x_n)$ be a function homogenous in ...
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2answers
52 views

what mathematical function we can use to show house price changes in time? [closed]

I want to know if I have data of house prices of an area in time, what mathematical function will best fit it's graph? Or in other word, what function I could use that in time $t$, $f(t)$ will be a ...
7
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1answer
92 views

Uniform bounds on rate of merging for Bayesian learners

Update. Cross posted at Cross Validated. In a well-known paper, Blackwell & Dubins (1962) show that the posterior probabilities of two Bayesian agents, whose priors agree on events of measure $0$,...
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1answer
657 views

Roy's identities for Stone-Geary utility functions

I'm having trouble showing Roy's identity for the following Stone-Geary utility function: $$U(x)=\prod_{i=1}^n\left(x_i-\gamma_i\right)^{\beta_i}$$ where $\sum \beta_i=1$ and $\gamma_i$ is the ...
8
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0answers
293 views

Local and Central Wage Bargaining: What Is the Difference?

Consider the following setting: Profit maximizing firms with production functions $\Pi(w,L)$, where $w$ is the wage and $L$ is employment. Unions who want to maximize the expected utility of their ...
3
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3answers
3k views

Alpha interpretation in Solow growth model

Consider the Solow model (without technology): $Y = F(K, L) = K^\alpha L^{(1-\alpha)}$ What's the economic interpretation of $\alpha$? Prove and argue the result. I see it as a share that ...
2
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0answers
220 views

Fisher Separation with negative interest rate

In class we discussed Fisher Separation which states that the investment decision is independent of the financing decision. The optimality conditions are that MRS = MRT = (1+i) (i = interest rate). ...